Mathematical Framework for Causal Reconfiguration in Discrete Topological Tensor Networks

This article develops a mathematical framework for causal reconfiguration in the discrete Spacecell network introduced in the original model paper and formalized in the companion mathematical foundations paper. We consider only the mathematical structure of the framework and do not address its physical interpretation. The scope is restricted to admissible network states, update structures, propagation constraints, and history-based variational concepts in a purely discrete topological setting. Explicit classes of update operators, update dynamics, continuum field equations, observable predictions, and numerical simulations are left for future work. No background spacetime manifold, metric structure, or continuum geometry is assumed. Causal update structure and topological reconfiguration are treated as fundamental. In this article, we study admissible configurations, local update operators, discrete update latencies, causal ordering rules, adjacency-restricted propagation, update cones, finite propagation depth, transport admissibility, and defect propagation. We also introduce admissible update histories, history-based action functionals, and stationary network evolutions. Local update events and chronograph-based ordering generate finite propagation structures without reference to continuum geometry. The resulting framework provides a mathematical foundation for future studies of structural propagation, defect dynamics, topological phase structures, and effective continuum descriptions emerging from discrete network evolution.